Is the following concept already known, perhaps with a different name?
Let $R$ be a commutative ring and $* : R \to R$ be an involutive homomorphism (the most typical case is $R=\mathbb{C}$ and $* = $ complex conjugation). A $\star$-module is an $R$-module $M$ equipped with an involutive homomorphism $* : A \to A$, where $A$ denotes the underlying abelian group of $M$, such that $(r \cdot a)^* = r^* \cdot a^*$ holds for all $r \in R$ and $a \in A$. This may also be described as a module over the twisted polynomial ring $R[T]_*$, in which $T r = r^* T$ (does this ring have a special name?). The tensor product over $R$ (!) makes the category of $*$-modules symmetric monoidal. The involution is defined by $(a \otimes b)^* = a^* \otimes b^*$.
Initially I wanted to represent the category of $*$-algebras as the category of algebras of a natural symmetric monoidal category, but the above candidate does not work: Algebras in that category satisfy $(a \cdot b)^* = a^* \cdot b^*$, but we would like to have $(a \cdot b)^* = b^* \cdot a^*$. Any ideas how to repair this?